Under the above assumptions, the modulating function 
Fp(y,t, +) is given by equation (9.67). Equation (7.51) of 
Chapter 7 modified by the requirement that the storm be of 
finite width has been employed, and the argument that shorter 
period waves require a longer time to travel from the rear edge 
of the fetch to the point, x = 0, y = 0, is employed. 
The square cutoff filter for the Gaussian case of a storm 
of finite width and duration over a fetch of finite length under 
the above assumptions, is then given by equation (9.68). The 
HM cutoff values are given by an equation similar to equation 
(7.57) except that they are determined by the distance R and not 
by xe The © cutoff values are given by equation (9.64). The 
# band width is given by equation (9.69), and the © band width 
is given by equation (9.70) in which R° equals x° + ye It should 
be noted that equations (9.64) and (9.70) hold only if R°>wW,“/4, 
that is, outside of a semi-circle with a center at x = 0, y =0, 
of radius W./2. If the point of observation is inside of this 
circle, the expressions for Ae, and Ae, given by equations 
(9.65) and (9.66) can be employed. The filter might be smoothed 
by arguments similar to those employed in deriving equation (7.61). 
The final forecast formulas for waves in deep water 
If the entire forecast is to be carried out in deep water, 
the final forecast formula is then given by equation (9.71). If 
the short crested disturbance at the source is given by equation 
(9.47), and if the disturbance is produced by a storm of finite 
width and finite duration over a fetch of length, F, then the 
forecast formula states that the short crested disturbance in 
S207 3 
